A sports car starts from rest at time t=0 seconds on a straight test track. Its acceleration is modeled analytically by the function a(t)=3t−2 (in m/s2) for 0≤t≤6. The position s(t) is measured from the starting line, with s(0)=0.
(a) Determine the car’s velocity v(t) for 0≤t≤6. Include appropriate units.
(b) Using your result from part (a), determine the car’s position s(t) for 0≤t≤6.
(c) Calculate the car’s speed and position at t=6 seconds.
(d) The car continues beyond t=6 seconds, but the acceleration function is no longer valid past this point. Without finding a new analytic formula, explain why the velocity you found in part (c) represents the instantaneous rate of change of position at t=6. Use correct calculus terminology in your explanation.